Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
800 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×#948 | C2 | semidirect |
| 3. #11723352 | C2 | semidirect |
| 4. #11722207 | C2 | semidirect |
| 5. #11722060 | C2 | semidirect |
| 6. #11722045 | C2 | semidirect |
| 7. #11722021 | C2 | semidirect |
| 14. C3×#3756 | C4 | semidirect |
| 15. C3×#3755 | C4 | semidirect |
| 16. C3×#3754 | C4 | semidirect |
| 17. C3×#3753 | C4 | semidirect |
| 29. C3×#948 | D3 | semidirect |
| 67. #3756 | Dic3 | semidirect |
| 68. #3755 | Dic3 | semidirect |
| 69. #3754 | Dic3 | semidirect |
| 70. #3753 | Dic3 | semidirect |
| 103. #948 | C3⋊D3 | semidirect |
| 220. C33 | #444 | semidirect |
| 309. C32 | #5145 | semidirect |
| 310. C32 | #5197 | semidirect |
| 347. C3 | #10591674 | semidirect |
| 348. C3 | #10592844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64159 | 2 |
| C32×#948 | 2 |
| #11723352 | 2 |
| #11722207 | 2 |
| #11722060 | 2 |
| #11722045 | 2 |
| #11722021 | 2 |
| #10592844 | 3 |
| #10591674 | 3 |